I am guessing that you mean in the movies, as there have been several DC/Marvel crossovers in the comics. As far as the movies go, this would be very doubtful unless either Warner Bros. (who own DC) or Disney (who own Marvel) ever decided to sell DC or Marvel to the other. But as long as they remain under different companies, it would be extremely unlikely to happen. Marvel can’t even use a large number of their own characters (like the X-Men) due to Sony or Fox having the movie rights.
But, there have been many crossovers in the comics, and we quite will see more in the future. Some of the notable crossovers you can find back issues of are:
DC vs Marvel (a.k.a Marvel vs DC)
Superman vs Spider-Man (there were two of these)
Batman vs The Hulk
JLA/Avengers
X-Men/New Teen Titans
Batman/Daredevil
Batman/Captain America
Batman/Punisher
Superman/Fantastic Four
Amalgam: During DC vs Marvel, the DC Universe and the Marvel Universe were merged and both companies on that week brought out books under the Amalgam banner (instead of Marvel or DC) which featured characters that were a mix of both a DC and a Marvel character. This proved popular enough that they did second Amalgam week later on.
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